Portraits always fail, at least if held to the highest standard: to ­re-create the person in full, the living, breathing, fully present being. They may be likenesses, sometimes uncannily so, but they are never adequate substitutes for what they represent.

And yet we continue making them, and the National Portrait Gallery’s triennial competition, the Outwin Boochever Portrait Competition, rewards artists who continue to struggle with the challenge. The results of this year’s contest, which winnowed more than 3,000 entries from across the United States down to an exhibition of 48 finalists — including works in video, sculpture, painting, drawing and new media — are on display at the gallery.

The winners were announced Friday: First prize went to Bo Gehring of Beacon, N.Y., who won $25,000 for a video titled “Jessica Wickham”; second prize went to Jennifer Levonian of Philadelphia for her video “Buffalo Milk Yogurt”; and Sequoyah Aono of New York won third prize for a self-portrait sculpture.

Portraiture is an inherently conservative medium. When the competition was first held in 2006, it didn’t include video art, and it still emphasizes artists working in the figurative tradition. But the focus, wisely, is on the process of making portraits, rather than the Portrait Gallery’s other mission, the memorialization of famous people. The parameters of what qualifies as portraiture have also been widened, and the show this year is a synoptic overview of how many serious and highly skilled artists are grappling with the old enigmas of making human likenesses.

The artists who this year rose to the top of the Boochever contest — a self-conscious attempt to imitate the annual competition held at London’s National Portrait Gallery — might be divided into those who concentrate on surface and those who look at depth, distinctions not to be confused with superficiality and profundity. The surface artists seem to accept the reasonable proposition that a visual medium can only register visual information, and so they struggle to find new ways to register that data. Often their focus is on flesh and details of flesh, with warts-and-all honesty. The depth artists are more interested in inchoate things, such as consciousness, memory or identity, using side channels and roundabout ways to gather and fix impressions.

The first-prize-winning video is in the surface category, rigorously so. Gehring, an artist with a background in science, slowly pans, at close range, to methodically document his subject, a friend and furniture designer, from toe to head. Jessica Wickham, dressed in blue-gray corduroys and a grubby, zip-up jacket, lies face-up on a cloth-covered platform while the camera scans her at such close range that the sides of her body can’t be contained within the frame. The timing of the camera’s motion is synced to a piece of music chosen by the subject, Arvo Part’s “Cantus in Memory of Benjamin Britten.”

The process suggests medical imaging, applied not to the interior mysteries of the body but its knowable surface. Wickham can be seen breathing under her clothes, and when the camera reaches exposed flesh, her hands and face, it registers all the imperfections. The power lies in the contract between the artist and the subject, the latter submitting to extraordinary scrutiny. Near the end, Wickham looks away from the camera, a tacit acknowledgment that there is something very uncomfortable about being the subject of Gehring’s camera.

Why do it? Perhaps to prove once again the limits of what we can know through portraiture, to demonstrate its failure in action: Here it is, the body, the subject, in all its detail. Is there anything else? Nothing more? Accepting the limits of our knowledge is one of the essential humilities of being human, and Gehring’s work dramatizes those limits. There is also a happy accident in the choice of music: Part’s composition consists of slowly repeated descending scales, while Gehring’s camera works up from the toes to the head. Taken together, these two metaphors of up and down, applied in different media, demonstrate how arbitrary most of our metaphors for measuring and defining human existence are, including the conceit that humans have both surface and depth.

Levonian’s second-place entry, “Buffalo Milk Yogurt,” is a wry animated piece using watercolor and cutouts to dramatize an existential crisis (a breakdown in a grocery store) experienced by the composer Corey Fogal, who also composed the soundtrack. It is a stream-of-consciousness gathering of impressions and odd sensations, the little things one notices when in a heightened state of emotional awareness. It also has an appealing absurdist sensibility, inviting you to notice bizarre details that make Levonian’s world pleasingly unsettled and strange. Odd groceries accumulate, including Pitbull Yogurt, suggesting an ironic take on the adage “You are what you eat,” and the protagonist returns home to put famous works of existentialism by Heidegger and Sartre onto a George Foreman Grill, perhaps a play on Claude Levi-Strauss’s distinction between the raw and the cooked.

Levonian’s piece leaves you with the sense that you know something about how she thinks. Or is it how her subject, Fogal, thinks? That dynamic, between the portrait as the product of an artist and the portrait as the trace of a person, is played out in myriad ways. Many of the artists, including third-prize winner Aono, opt to bypass that fundamental tension by making self-portraits. Aono’s sculpture is appealingly objective, a life-size image of a painfully self-conscious man standing with arms at his sides. Made in part with a chain saw, and other more-refined tools, parts of it feel rough and unfinished, yet the whole is strikingly lifelike and unsettling.

Washington, D.C.-based artist Caitlin Teal Price goes to what might be the other extreme from self-portraits: photographing women she doesn’t know, choosing locations that emphasize the anonymity of the encounters. Her entry, “Leslie,” shows a woman in young middle age, with a light layer of makeup, captured under a highway overpass in New Orleans. A broad patch of bright illuminates what the makeup is meant to hide, the fine creases in the lips, the slight bagginess around the eyes. Although the subject doesn’t wear a lot of makeup, the heightened sense of her self-presentation makes the face seem like a mask.

Throughout the exhibition, there is a palpable anxiety about the photograph and how it seems to offer and then fails to deliver on the promise of truth. Photo-realism is a popular approach, and some artists go to astonishing lengths to embrace and reject the photograph at the same time. Kumi Yamashita’s “Constellation — Mana” is based on a snapshot of her niece, whom she describes as “chatty, awkward and sometimes obnoxious.” From a distance, the portrait appears to be a photograph that has been slightly altered to give its surface the look of a lightly crackled pottery glaze. Closer inspection reveals the astonishingly complicated method of its production: A single fine string has been wound around hundreds of delicate nails, giving a sense of the missing snapshot through the density of the web it creates.

Where is the surface of this image? Is it the thread itself, woven a few millimeters above the wood panel? Or is it the snapshot, which we never see, about which the artist says, “I wanted to stare at this face for a long time.”

Yamashita’s work is delightful, and her brief, clear, sincere artist’s statement even more so (“This is a portrait of my niece, Mana”). Too many of the artists in this exhibition fall back on art as a form of self-therapy, too many write in cliches or indulge in the sloppy, non-thinking of art-school discourse. Yamashita honestly acknowledges the fascination the photographed face has for her, that by creating a facsimile of it, she can hold it in the mind longer. The process extends her encounter with the elusive meaning of the photograph, yet results in a work that is fresh and accessible, and appeals without background on the subject.

The Boochever Competition is held so infrequently that it’s easy to forget it exists, but the winners this year suggest it is growing in sophistication, with invigorating results.

Outwin Boochever Portrait Competition 2013

Finalists can be seen at the National Portrait Gallery through Feb. 23. For more information, visit npg.si.edu.